a number is increased by 20% and then it is decrease by 20% find the net increase or decrease per cent?
Answers
Question :— A number is increased by 20% and then decreased by 20%. What is the net increase or decrease percent.
Assume that the number is 100. Then, 20% of 100 is 20×100100 = 20. Increasing 100 by 20% means increasing 100 by 20 and the resultant number is 120.
Now the new number is 120. 20% of 120 is 20×120100 = 120/5 = 24. Thus decreasing 120 by 20% means same as subtracting 24 from 120 and the resultant number will be 120 — 24 = 96.
Since 96 is less than 100, the original number, net decrease
=100−96100×100
=4100×100
=4
Thus the net decrease is 4%. It is true for all other numbers.
Let us suppose the number to be x.
As per the first case, the number is increased by 20%
Hence: x+ ((x*20)/100)
Resultant number is ‘6x/5’
As per the second case, resultant number is then decreased by 20%
Hence : (6x/5) - (((6x/5) * 20)/100)
Which is (6x/5) - (6x/25) = 24x/25.
The original number being x, we witness a net decrease in the overall process as (24x/25) is less than x.
Therefore Net decrease_
x - (24x/25)= x/25
Net decrease in percentage= (Net Decrease/ Initial Value) * 100%
Thus, ((x/25)/x) * 100% = 4%
So, the answer is 4%.
Step-by-step explanation:
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